Vincen wrote: ↑Mon Sep 14, 2020 3:09 am
If cube \(X\) has an edge of length e and cube \(Y\) has an edge of length \(e + 1,\) how much greater is the total surface area of cube \(Y\) than that of cube \(X?\)
A. \(12e + 6\)
B. \(6(e + 1)2\)
C. \(e + 1\)
D. \(e\)
E. \(1\)
Answer:
A
Source: GMAT Prep
These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.
Let's say e =
3
Cube X
Each edge has length
3
Since each face of the cube is a SQUARE, the area of ONE face =
3² = 9
So, the area of all SIX faces = (6)(9) =
54
Cube Y
Each edge has length
3 + 1. So, each edge has length 4
Since each face of the cube is a SQUARE, the area of ONE face = 4² = 16
So, the area of all SIX faces = (6)(16) =
96
How much greater is the total surface area of cube Y than that of cube X?
Difference =
96 -
54 =
42
So, when we INPUT e =
3, the answer to the question (i.e., the OUTPUT) is
42
Now we'll examine each answer choice, to see which one yields and output of
42 when we replace e with
3
We get:
A. 12(
3) + 6 =
42 Great! Keep.
B. 6(
3 + 1)² =
24. We want an output of
42. ELIMINATE B
C.
3 + 1 =
4. We want an output of
42. ELIMINATE C
D.
3 =
3. We want an output of
42. ELIMINATE D
E. 1 =
1. We want an output of
42. ELIMINATE E
Answer: A
Cheers,
Brent
